A DC9-50 FLC IS DIRECTED TO CLB TO THE SAME ALT THAT AN ACR F100 IS CLBING TO AND THEY HAVE A CLOSE ENCOUNTER.

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WE WERE LEVEL FL220 DIRECT RST. ATC CALLED TFC AT 12 O'CLOCK AT FL220. WE SAW THE ACFT ON THE TCASII JUST COMING INTO VIEW AT 6 MI. IT INDICATED -200 FT. ATC DIRECTED US TO CLB TO FL230; SO I STARTED TO CLB AND BOTH ME AND MY FO VISUALLY SAW AN AIRPLANE TO OUR R OF CTR. WE BOTH SAW THAT HE WAS NOT CONVERGING WITH US; BUT TURNING AWAY. ATC DIRECTED A L TURN TO US; BUT I SAW THE FOKKER JET TO OUR R AS ATC WAS ISSUING US THE EVASIVE VECTOR AND WE TOLD ATC WE SAW THE OTHER AIRPLANE. OUR TCASII WAS DIRECTING US TO 'DSND NOW;' BUT I LEVELED AT FL230 AS WE PASSED THE JET AT FL230. I ASKED THE ATC CTLR WHY SHE TOLD US TO CLB AND SHE SAID THE JET WAS COMING FROM ANOTHER SECTOR AND WAS TOLD TO CLB FROM FL210 TO FL240. I WAS TOO EXCITED TO ASK HER WHY SHE HAD DIRECTED US TO CLB; BUT SHE INITIALLY SAID THE OTHER JET WAS AT FL220. OBVIOUSLY THE JET WAS STILL CLBING; BUT SHOULDN'T SHE KNOW THAT FROM HER COMPUTER DISPLAY SHOWING ALT READOUTS? SUPPLEMENTAL INFO FROM ACN 430463: DURING CLB WITH AUTOPLT ON; RECEIVED CLRNC TO CLB TO FL230. THIS WAS HEARD BY BOTH CREW MEMBERS; RESPONDED TO ATC AS FL230 AND IN ACCORDANCE WITH ACR PROCS; CONFIRMED AND POINTED TO THE ALT WINDOW AND VERIFIED. PASSING APPROX FL217 IN VFR CONDITIONS; A TCASII ADVISORY WAS RECEIVED; FOLLOWED BY A CLB COMMAND. THE ACFT WAS SPOTTED AND A SLIGHT L TURN WAS MADE AND THE CLB WAS CONTINUED UNTIL CLR OF CONFLICT WAS GIVEN. ATC ASKED US OUR ALT AND WE HAD RECOVERED AT FL230. THEY LEFT US AT FL230 AND THE FLT CONTINUED UNEVENTFULLY TO ORD.